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Friday, November 16, 2012

Bs→ µ µ: a hint of rare beauty

This week the LHCb collaboration has reported publicly (http://arxiv.org/abs/1211.2674) a new measurement on the rare decay $B^0_s \to \mu^+ \mu^-$.
As I am part of this collaboration and have given my little contribution to this result, I feel obliged (and honoured) to give a quick explanation of why this result is important.
Note: what follows is more pedagogical than usual, so I will not try to be too precise.

Figure 1 An event with two muons at LHCb

Why we want to see it

The $B^0_s$ is one of the various type of particles produced when smashing protons at the Large Hadron Collider (LHC) in Geneva.
This particle is composed of two quarks ($s$ called strange and $\bar b$ called beauty) with same but opposite charge but different type (or flavour). If they had also same type they could annihilate one with each other and transform in a photon or something similar. The photon could then transform into two electrons with opposite charge, or into two muons, which are the fatter brothers of electrons.
But $s$ and $\bar b$ are of different type and in order to transform into something neutral and then into two muons something "in between" is needed.
Only few and complicated ways are present to make this transition possible and involve many smaller transitions, with various particles in them. This can be predicted with quite some accuracy and gives a theoretical probability for this decay to occur of 3.5 times every billion decays of $B^0_s$.
That is why we are talking about rare decays!
What said holds for the presently most accepted theory of particle physics, called Standard Model.
Now, if the Standard Model is not the best theory to explain nature, then maybe we are missing other pieces, other particles which can give contributions to this rare decay allowing an easier transition between the $s$ and $\bar b$, inside the $B^0_s$, to the two muons.

How we try to see it

We would like to see these decays as they happen, but the $B^0_s$ decays so quickly that we can only see its decay products, the muons in this case.
The muons are easy to see: they are charged so they leave a track in our detector and they travel through a lot of material so that we can recognize them by stopping all the other particles with iron walls (literally).

So while LHC is smashing protons we take data out of our detectors and we analyze them.
One of these collisions is shown as seen by the LHCb detector in the first figure where two muons are visible in magenta.
So we take all the muons from each collision and combine them in pairs.
Now, many muons are present in these high energy collisions, so that if you take two random muons that left tracks in your detector and combine them their combined mass will be also (almost) random.
But we already know the mass of the $B^0_s$ particle so we know where to look and we can calculate quite accurately the number of random combinations at this mass (called background), all in excess of this is what we call a signal: a proof that the considered decay exists in nature.

What we did see

We indeed have seen an excess of events with mass around the $B^0_s$ mass.
An example is shown in the second figure which displays the distribution of combinations as a function of the mass.
The black dots with bars are the data points, the dashed blue line is the random background and the red peak is the signal we have estimated.
(I will not explain here the other components).

Figure 2 Distribution of the mass of the muon pair

How much are we sure that this is really our decay? Well we calculated the probability of this signal being appeared just by chance (i.e. just by a fluctuation of the random background) and it is $\frac{5}{10000}$ so that we can claim this is the first evidence of this decay... after a search which started almost 30 years ago (the first search for this decay was in 1984).

What we conclude

The measured probability of $B^0_s$ to decay in two muons is $3.2^{+1.5}_{-1.2}\cdot 10^{-9}$ (3.2 in a billion) very close to the Standard Model prediction of $3.5\cdot10^{-9}$; but the uncertainties are still very large so that more measurements will be needed to assess whether this is just Standard Model and excludes completely some other models of new physics or something new is there: but already seeing this elusive decay is a big step towards a knowledge of what is hidden in this rare beauty.